This solution certainly looks mathematically correct and efficient.
On the other hand, there are serious problems with its consistency,
especially at the high energy scale, where the fourth-derivative
terms gain the magnitude comparable to the GR action. On top
of that, there is a problem with the uniqueness of the procedure.
E.g., one can modify this effective approach to include an \(R^2\) 
term, or any \(f(R)\)  term, into the main part of the action,
because these terms do not produce a ghost. The same concerns
many other terms, e.g., all \(\mathcal {O}(R^3_...)\) 's. At the same
time, it should be strictly forbidden to do the same with the
\(R\operatorname{\square }R\) -term, which produces a scalar ghost. As it was discussed
in [1]} and also in [2]}, the analogy with QED and
the standard resolution of the problem of “run-away solutions” is
not convincing. So, all the scheme looks as an ad hoc
procedure, without the physical background. It is as saying that we
do not like ghosts and will therefore forbid them. If we follow the
same approach in other branches of QFT, it is perfectly well
possible to modify any theory in a way we like and provide the
predictions we like. Despite this may look a universal solution of
all the problems, the theories created in this way would not be
reliable or, better say, would not provide reliable predictions.
